O‘zbekiston matematika jurnali 70-том 1-нөмір (2026)

High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations

Aripov, M., Utebaev, D., Kdirbaev, S.

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Аңдатпа

In the article, high-accuracy difference schemes for the Cauchy problem for a system of fourth-order equations are obtained. Based on the method of energy inequalities, the stability of the scheme is proved, a priori estimates of the solution to difference schemes are obtained, and their convergence and accuracy are proved. The results obtained for the system are applied to solve the first initial-boundary value problem for the equation of ion-acoustic waves in a "magnetized" plasma for the generalized potential of the electric field. The schemes constructed for this problem have second-order accuracy in spatial variables and fourth-order accuracy in time variables. In energy norms, convergence and accuracy estimates are obtained in classes of smooth solutions.

Cauchy problemfourth-order system of equationsion-acoustic wave equationdifference schemesapproximation errorstabilityconvergenceaccuracy

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Дәйексөз алу

APA 7 
Aripov, M., Utebaev, D. & Kdirbaev, S. (2026). High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations. O‘zbekiston matematika jurnali, 70(1).
GOST R 7.0.5 
Aripov, M., Utebaev, D., Kdirbaev, S. High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations // O‘zbekiston matematika jurnali. 2026. Т. 70. № 1.
BibTeX 
@article{m.2026,
  author  = {Aripov, M. and Utebaev, D. and Kdirbaev, S.},
  title   = {High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2026},
  volume  = {70},
  number  = {1}
}
RIS 
TY  - JOUR
AU  - Aripov, M.
AU  - Utebaev, D.
AU  - Kdirbaev, S.
TI  - High-accuracy difference schemes for solving non-stationary fourth-order equations and their application to non-classical partial differential equations
JO  - O‘zbekiston matematika jurnali
PY  - 2026
VL  - 70
IS  - 1
ER  -